Economic Considerations for Sizing Tubing and Power Cable for Electric Submersible Pumps Maston L. Powers, SPE, Conoco Inc.

Summary. Power consumption of an electric submersible pump (ESP) installation may be categorized into three components: the energy required to perform useful work, which is equivalent to the net hydraulic load divided by the product of pump and motor efficiencies; the energy absorbed by tubing friction, which is equal to the dissipated hydraulic energy divided by the efficiency product; and power-cable electrical losses. An improved design technique is presented that brings the first two categories into economic perspective. The interrelated effects of tubing friction, power-cable resistance, and motor voltage on ESP power consumption are demonstrated, as is the degree of desirability for using a motor of the highest available voltage. An equation, useful in making economic evaluations of alternatives, is developed for calculating power consumption for combinations of tubing size, power-cable size, and motor voltage. Variations of power consumption are illustrated graphically for various combinations of these three parameters. Also illustrated is the effect of the nature of a specific net hydraulic load-Le., the product of rate, net lift, and specific gravity. Practical examples using the design techniques developed here are presented and comparisons made to designs based on common practice.

Introduction Sizing of tubing and power cable for ESP's has not received at-tention commensurate with the inherent effects on energy con-sumption and the resultant costs. Common practice is to select sufficiently large tubing that head loss will not exceed 100 ft/l ,000 ft[1O mllOO m] and power cable of adequate conductivity to limit voltage drop to 30 VII ,000 ft [30 V/305 m]. A calculation is also made to determine whether the chosen cable permits adequate motor terminal voltage during starting conditions. It is demonstrated that these criteria permit frictional energy losses of up to 10% of net hydraulic load and dictate electrical energy losses that vary directly with depth cubed and inversely with motor voltage squared. An alternative basis for cable selection limits voltage drop to 5 % of motor nameplate voltage. 1 Practical examples show that these criteria may not produce a viable design in some circumstances. Frequently, the tubing used in an ESP installation is inherited from a previous sucker-rod pumping system. An example is presented to demonstrate that this situation could result in a tubing string of superfluous flow capacity and insufficient clearance for the instal-lation of an adequate power cable. Presently used bases for tubing and power-cable selection will normally result in a mechanically functional system, although not necessarily the most economical one at current electric power costs. Furthermore, these bases do not recognize the interrelated effects of tubing friction, power-cable resistance, and motor voltage on ESP power consumption, nor do they address optimization of equipment selection to produce minimum cost. In succeeding sections, the contribution of these three factors to power consumption is investigated and a basis for optimum equipment selection is developed.

PowerConsumptlon Equation The net hydraulic load of an ESP represents the specific task for which the system was designed and installed. This quantity equals the product of producing rate, net lift, and fluid specific gravity; the associated power consumption is equivalent to this product divided by pump and motor efficiencies. Total power consumption, PT, of an ESP installation may be separated into three components: the net hydraulic load power requirement, Ph; power consumed by tubing friction, Pf' which is equal to the dissipated hydraulic energy divided by the product of pump and motor efficiencies; and electrical losses in the power cable, Pe . The sum of Ph and Pf equals the total hydraulic load power requirement, PH, which is equivalent to motor input power; the sum of P f and P e represents

Copyright 1988 Society of Petroleum Engineers

SPE Production Engineering, May 1988

total power losses, PL> exclusive of pump and motor efficiency losses attributable to Ph' Mathematical expressions for PT, Ph, Pf' Pe , PH, and PL are developed in Appendix A, as is an expression for normalized total power consumption, P n' defined as PT+Ph. Thus, P n represents total power consumption expressed as a mul-tiple of the power applied to the performance of useful work. Therefore, it is indicative of how efficiently power is used. A P n value of 1.0 is equivalent to an efficiency of 100%, exclusive of pump and motor efficiencies; larger values indicate decreasing ef-ficiencies.

The two terms of total power consumption as expressed in Eq. A -10 are equal to PH and P e' respectively. The difference between surface tubing pressure, PI' and pump inlet pressure, Pi, appears in a parenthetical expression common to each term. The values of these two quantities are generally small compared with the total dynamic head and furthermore tend to cancel each other. Therefore, ignoring the effects of these for the purpose of analyzing the effects of all other variables on power consumption does not result in sig-nificant error in most circumstances. Thus, for all practical purposes, the first term of PT is proportional to producing rate, q, fluid specific gravity, "I, pump setting depth, D k> and (l,ooo+HL) or (1,000+Kf dt - 5); it is inversely proportional to the product of pump and motor efficiencies, EpEm. The quantity Kf dt-

5 is a close approximation to head loss, HL . Setting depth was expressed in 1,000-ft [305-m] units in the derivations of Ap-pendix A because head-loss data are commonly presented in feet per 1,00P ft [305 m]. Likewise, electrical property data of con-ductors are commonly expressed on a I,OOO-ft [305-m] basis. Ap-plying the preceding analysis to the second term of Eq. A -I 0 reveals that cable-power loss is proportional to q2, "1 2 , Dk 3 , (I,OOO+HL)2 or (I ,000 + Kfdt -5)2, and the conductor resistance, Tk, or the reciprocal of conductor area, Ac -1; it is inversely proportional to the squares of motor voltage, Vm , power factor, Fp , pump effi-ciency, Ep' and motor efficiency, Em' Values of Tk conforming to the recommended maxima2,3 can be determined from Table 1.

The interrelated effects of tubing friction, power-cable resistance, and motor voltage on total power consumption become obvious from the preceding discussion or may be inferred directly from Eq. A-10. The first term of PT is a function of only one of these three variables. Head loss caused by tubing friction appears in the factor (I ,OOO+HL ). The second term is a function of all three variables. Head loss occurs in the same factor as in the first term; however, this factor is squared. Power-cable resistance is a direct multiplier of the second term. Most dramatic is the effect of motor voltage,

217

TABLE 1-TYPICAL PROPERTIES OF COPPER POWER CABLE

AWG Ac rk at 140F" Xk at 60 Hz"" Kvat 1400 Ft Size (cir mils) (0/1,000 It) (0/1,000 It) (VIM ,000 It)

8 16,510 0.781 0.0459 1.167 6 26,240 0.489 0.0427 0.744 4 41,740 0.308 0.0399 0.481 2 66,360 0.199 0.0362 0.321 1 83,690 0.158 0.0352 0.261

1/0 105,600 0.126 0.0341 0.214 2/0 133,100 0.101 0.0332 0.177

'Values of r, at other conductor temperatures, T, can be calculated by multiplying the tabulated data by the factor [t +0.0019(T-140)], from Ref. 6, Pages 15-6 and 157. Resistances presented here correspond to the maximum allowed by Refs. 2 and 3. .

'To obtain values of X, at other frequencies, multiply the tabulated data by the quotient of frequency/60. 'Voltage-drop coefficients, K v' were calculated assuming Fp =0.83, T= 140oF, and a frequency of 60 Hz. Values of K v at other power factors and for other conditions can be calculated with K v = Y3(r, cos 6 + X, sin 6).

the square of which appears in the denominator. Thus, an increase in motor voltage significantly decreases the value of this term.

An obvious conclusion from the preceding analysis is that the highest available motor voltage is the most desirable. Not only will the use of a higher-voltage motor reduce power consumption, it will in many instances result in a smaller and thus cheaper power cable as the optimum size. An illustrative example is presented later. In the case of a new installation, the only cost associated with a higher-voltage motor would be a somewhat greater investment for a motor controller of adequate voltage rating. An inadequate power-distribution system or a restrictive local ordinance would be the only justifiable reasons for not using the highest-available-voltage motor for a new installation. It has been suggested that high-voltage motors may lack the longevity oflower-voltage motors. This sug-gestion is neither confirmed nor denied; however, even if it were true, instances in which motor insulation life was the ultimate cause of failure would be relatively infrequent. In the case of a replacement motor in an existing installation, a change to a higher voltage might involve investments for replacing transformers and the motor con-troller. In this event, an economic analysis would be required to determine whether the resultant power savings would justify the required expenditure.

Effects of the common practice of selecting tubing size on the basis of a maximum head loss of 100 ft/l ,000 ft [10 m/IOO m] and selecting power cable based on a maximum voltage drop of 30 V 11 ,000 ft [30 V 1305 m] may be inferred from the equations of Appendix A. It may be observed from Eqs. A-I and A-2 that a head loss of 100 ft/l,OOO ft [10 m/IOO m] would result in a fric-

~ I

.....

Z 1&1 a: a: J (.) cIS a: o t;

~ a: 1&1

~ o a...

>-(.) Z 1&1 (.) ii: Lt. 1&1

218

OL---~20~---4~O~--~6~O----8~O~---IOO~--~120 MOTOR LOAD - % OF FULL LOAD RATING

Fig. 1-Typical motor characteristics.

tional energy loss of 10% of net hydraulic load. Eq. A-8 indicates that fixed voltage-loss criteria, such as 30 V/l,OOO ft [30 V/305 m], would result in electrical energy losses that vary directly with depth cubed and inversely with motor voltage squared. The preceding observations assume that PI ana Pi are approximately equal or relatively small.

It has been mentioned that both pump and motor efficiencies appear in the denominator of the first term of the power-consumption equation (Eq. A-I 0) and that the squares of the power factor and efficiency product appear in the denominator of the second term. This demonstrates the necessity of operating a pump and motor at conditions of high efficiency and power factor if power consumption is to be minimized. High pump efficiency is ensured when a pump is selected that will deliver the design rate at near peak efficiency.

Current, Power Factor, and Efficiencies Use of the techniques presented here requires that the running current, power factor, and pump and motor efficiencies be known. Pump efficiencies are readily obtainable from plots of efficiency vs. producing rate furnished by pump manufacturers. Current, power factor, and motor efficiency depend on motor loading. Presented in Fig. 1 are typical values of these three variables plotted

Z 0 t= a... :& ;:) en z 0 u a: 1&.1

~ a...

...J ~ 0 l-e 1&.1 N ...J < :& a: 0 z

1.4 8 6

, , ,

CONDUCTOR AWG SIZE 4 2 1/0

TYPICAL ESP RATE 4000bbllD

NET LIFT 2000 It 3112 in. 00 TUBING

COPPER CONDUCTORS

NO-START LINE

2/0

1.0L..~20~--------6.1.0----------101..0--------.....J140 CONDUCTOR AREA ( 1000 ~ MILS)

Fig. 2-Effect of motor voltage: high rate/shallow depth.

SPE Production Engineering, May 1988

1.4 8 6

,

z ' Q ' I- , ~ , ::> 1.3 , C/) Z o (.) a:: w

~ ..J g I-o W N ..J 1.1 C/) z 0 (.) a:: w ~

~ ..J

~ 0 I-0 W N :::i

CONDUCTOR AWG SIZE 4 2 1/0 210

z 0

~ TYPICAL ESP Q.. ~ RATE' 2000bbi/D ::;) NET LIFT 4000 ft (/) z 1300 V MOTOR 0 COPPER CONDUCTORS 0 a:: I.LI

~ 0 Q.. 1.2 ...J ~ 0 ....

0 I.LI N ...J 1.1 ct

~ a:: 0 z

I.O .... ~----~:------~----~ 20 60 100 140 CONDUCTOR AREA ( 1000 J1 MILS)

Fig. 6-Effect of tubing size: medium rate/medium depth.

Graphic illustration of Combined Effects

The combined effects of tubing size, power-cable size, and motor voltage on power consumption are illustrated graphically in Figs. 2 through 7. From these, the effect of the nature of a specific net hydraulic load can also be inferred. In the preparation of these six figures, Pi and PI were assumed to be equal or negligible. Values of 0.82 and 0.85 for motor power factor and efficiency, respec-tively, were also assumed. Pump efficiencies were selected from Table 2. Copper conductors were used, and combinations of producing rate and net lift were selected to result in a constant net hydraulic load throughout this development. Figs. 2 through 4 contain plots of Pn vs. Ac and American wire gauge (AWG) size for motor voltages of 1,000, 1,300, 1,700, and 2,200 V for com-binations of producing rate, net lift, and tubing size of 4,000 BID, 2,000 ft, and 3.5 in. [636 m3 /d, 610 m, and 8.9 cm]; 2,000 BID, 4,000 ft, and 2.875 in. [318 m3/d, 1219 m, and 7.3 cm]; and 1,000 BID, 8,000 ft, and 2.375 in. [159 m3/d, 2438 m, and 6.03 cm], respectively. Tubing sizes commensurate with flow rates were used in these three examples to suppress the effects of head loss so that the contribution of all other factors would not be obscured. The degree of desirability of using the highest available motor voltage can be observed from each of these three figures, which

CONDUCTOR AWG SIZE 1.4 8 6 4 2 1/0 2/0

, \ z \\ 0 \ \ TYPICAL ESP ~ RATE' 1000bbi/D Q.. \ \ ~ \ \ NET LIFT '8000 ft ::;) I. 1300 V MOTOR (/) \ \ z COPPER CONDUCTORS 0 \ 0 a:: \ I.LI

~ Q.. 1.2 ...J ~ 0 ....

0 W I.LI ~ N

...J :::; 1.1 ct !-Il:: ~ :! a:: 0 en z I 0

Z

I.O ..... ~-----'------'-----.... 20 60 100 CONDUCTOR AREA ( 1000 rJ MILS) 140

Fig. 7-Effect of tubing size: low rate/great depth.

illustrate that the effect of motor voltage is magnified when con-ductor area diminishes. This could be anticipated from Eq. A-II, because the square of the motor voltage appears in the denominator of the second term and conductor resistance appears in the numerator. Comparing Figs. 2 through 4 illustrates that the need for higher-voltage motors becomes progressively greater as the nature of the net hydraulic load shifts to greater depths. Fig. 4 shows (1) that the power consumption of a system using ai, 000-V motor installed at a depth of 8,000 ft [2438 m] would be 13 % greater than that of one using a 2,200-V motor if A WG Size I cable is used and (2) that the use of Size 2 or smaller cable would prohibit the starting of a 1,000-V motor under the conditions assumed in this example.

Figs. 5 through 7 contain plots of P n vs. A c and the A WG size for various tubing sizes and for the same values of producing rate and net lift on which Figs. 2 through 4, respectively, were based. A constant motor voltage of 1,300 V was used in the preparation of Figs. 5 through 7 so that the effects of motor voltage would be suppressed, thus allowing the effects of tubing size, conductor size, and the nature of the net hydraulic load on power consumption to be more easily distinguished. A pronounced effect of tubing size on power consumption is demonstrated in Fig. 5. Under the con-ditions assumed in this example (4,000 BID [636 m3 /d] and 2,000-

TABLE 2-PUMP DATA USED IN PRACTICAL EXAMPLES

SingleStage Performance at Operating Rate

Operating Brake Average Cost Rate Head Efficiency Horsepower" Per Stage

Pump Type (BID) J!!L (%) (hp) ($) 5.5-0600 600 26 58 0.198 30 5.5-0750 750 25 58 0.238 31 5.5-1000 1,000 20 58 0.254 32 5.5-1500 1,500 19 60 0.350 34 7.0-2000 2,000 40 64 0.920 60 7.0-4000 4,000 36 68 1.559 130

'These numbers assume a specific gravity of 1.0 and must be multiplied by the fluid specific gravity if it differs from 1.0.

220 SPE Production Engineering, May 1988

START

SELECT NEXT SMALLER SIZE CABLE (THE

OPTIMUM FOR CONSIDERED TUBING SIZE)

Fig. a-Design-procedure flow chart.

ft [61O-m] net lift), the power consumption with 2.375-in. [6.03-cm] tubing is 30% more than with 4.5-in. [II.4-cm] tubing, as-suming that A WG Size 2 cable is installed. Significant effects of tubing size are also present at the 2,000-BID [318-m3 Id] producing rate and 4,000-ft [l219-m] net lift depicted in Fig. 6; however, the effect of tubing size over the entire range from 2.375 to 4.5 in. [6.03 to 11.4 cm] is minimal under the conditions presented in Fig. 7 (l,OOO-BID [I59-m 3 /d] producing rate and 8,000-ft [2438-m] net lift).

No-start lines are traced on Figs. 2 through 4,6, and 7. For Fig. 5, the no-start line fell outside the depicted area. The no-start lines of Figs. 2 through 4 are the loci of marginal starting points for assumed motor voltages and for the tubing size designated on the respective figures. In an extension of Fig. 5 and in Figs. 6 and 7, the no-start lines are the loci of marginal starting points for an assumed voltage of 1,300 V and for various tubing sizes. The P n-vS.-Ac curves become dashed lines after intersecting the no-start lines of all figures, indicating that motor starting will likely be a problem. The no-start lines of Figs. 2 through 4 were plotted by assuming various cable sizes and determining values of rk and K v from Table 1. Eq. B-4 was then used to calculate corresponding values of V m for marginal starting conditions. These were sub-stituted into Eq. A-II, along with a value of H L representative of the tubing size designated on the respective figures, to calculate values of P n corresponding to each assumed cable size. Values of 4.0 and 0.5 were assumed for Fls and!vs, respectively, in the preparation of all six figures. The no-start lines of Figs. 6 and 7 were plotted by calculating values of PH for each tubing size with Eq. A-3 and substituting these and the assumed motor voltage of 1,300 V into Eq. B-3 to calculate values of Kv at marginal starting conditions. Corresponding values of Ac and rk were then interpo-lated from Table 1. Values of rk and H L were then substituted into Eq. A -11 to obtain values of P n corresponding to the interpolated values of Ac for each tubing size.

SPE Production Engineering. May 1988

TABLE 3-COPPER CONDUCTOR AMPACITY RATINGS

AWG Size

1 2 4 6

Ampacity Rating Polypropylene E-P Rubber

Insulation Insulation 94 110 82 94 61 70 46 53

Design Procedure With the Power-Consumption Equation Eq. A-I 0 implies that an ESP could achieve a minimum power con-sumption approaching Ph if sufficiently large casing were used to permit installation of very large tubing and power cable. It is likely that such an installation would be neither mechanically nor eco-nomically feasible; however, the optimization procedure presented for an existing well could be extended to include the drilling and completion of a well to be equipped with an ESP system designed for specific conditions. The design procedllre outlined below and illustrated in Fig. 8 considers both investment and operating costs. Necessary data include a knowledge of well performance, well casing size and weight, completion interval, produced-fluid spe-cific gravity, surface tubing pressure, unit power cost, and equipment prices.

Proper application of the power-consumption equation will result in the most economical ESP system for performing any specific job. As is standard procedure, a pump of the largest series that will fit inside the well casing and deliver the design producing rate at near peak efficiency is selected. The smallest tubing size that will result in a head loss ofless than 100 ft/l ,000 ft [10 m/100 m] is tentatively selected. Tubing of smaller diameter and lesser joint strength than 2.375-in., 4.70-lbm/ft [6.03-cm, 7.0-kg/m] J-55 upset should be avoided if possible. Each tubing string considered must have adequate tensile strength to support its own weight, the cable's weight, and the hydraulic force. A tentative pump and motor design is developed next in the normal manner with a value of HL corre-sponding to the design producing rate and tubing size, appropriate value for Pi- Pt' and 'Y, and a knowledge of well productivity. A motor of the highest available voltage should be selected. Next, a power cable of adequate ampacity is tentatively selected to fit in the clearance between the casing ID and the tubing coupling OD that will result in a voltage drop of less than 30 V/I,OOO ft [30 V 1305 m] if feasible, or otherwise the smallest possible voltage drop. Maximum cable size for various combinations of tubing and casing are recommended in Ref. 1. Voltage drop per 1,000 ft [305 m] is equal to the product IK v. Values of K v can be observed for a conductor temperature of 140F [60C] or calculated for other tem-peratures with Table 1. Recommended ampacity ratings23 are presented in Table 3. The cost of the entire installation can then be calculated. The next step is to calculate the power consumption of this system with Eq. A-lO. The annual power cost can be com-puted with this quantity and the unit power cost. This procedure should be repeated with the next larger cable size. The additional investment for the larger cable should then be divided by the re-sulting reduction in annual power cost to determine the capital recoupment period. If the result is less than about 3 years, the next larger cable size should be tentatively selected and the procedure repeated. These iterations should be continued until an increase in cable size no longer results in an acceptable payout. The largest cable that provided such a payout over the preceding smaller size is the one of choice. Cables smaller than the initial selection need be considered only if the first comparison does not show an ac-ceptable payout. More rigorous economic analyses than that presented above could be developed; however, the effort might not be warranted. Prediction of cable life would be essential for such analyses. A reasonable cable life under average well conditions might be 10 years. However, elevated temperatures and pressures and the presence of H2S can drastically reduce cable life, as can mishandling and other sources of mechanical damage. Conse-quently, predicting cable life is subject to considerable uncertainty .

221

TABLE 4-MOTOR DATA USED IN PRACTICAL EXAMPLES

Nameplate Nameplate Full-Load Full-Load Horsepower Voltage Amperage Efficiency Power Cost

Type (hp) (V) 5.5 50 1,200 5.5 70 1,150 5.5 80 1,300 5.5 130 1,700 5.5 130 2,200 7.0 85 1,300 7.0 100 700 7.0 100 850 7.0 100 1,100 7.0 100 1.700 7.0 120 2.200

TABLE 5-TVPICAL TUBING AND CABLE PRICES USED IN PRACTICAL EXAMPLES

Tubing Sizes Cost in. Ibm/ft ($/ft)

2.375 4.70 3.20 2.875 6.50 4.00 3.500 9.30 5.50

Cost Cable Size ($/ft)

1 5.00 2 4.40 4 3.00 6 2.40

Determining tubing life would also be necessary but would not be as critical because it would normally be a longer, more easily pre-dicted period.

Up to this point, the most economical cable size has been deter-mined for only the initial tentatively selected tubing size. The next larger tubing size should now be selected and the entire procedure outlined above repeated, including the determination of the number of pump stages and motor horsepower. As before, adequate clearance within the casing is essential. The most economical design incorporating the larger tubing size will always be more expensive than the one using the smaller size. The additional investment should be compared with the resulting annual power cost savings as done previously. If a capital recoupment period of less than 3 years is evident, the next larger tubing size should be similarly investigated. Because the initially considered tubing size was the smallest that would result in a head loss of less than 100 ftll,OOO ft [10 mllOO m], there is no need to analyze systems with smaller-diameter tubing. This can be inferred from examination of Eq. A-lO and is demonstrated in Case 1 of the practical examples.

(A) 26 38 39 40 31 41 88 73 56 36 34

(%) Factor ~ 84 0.82 14,000 84 0.82 17,000 84 0.82 19,000 84 0.82 32,000 84 0.82 32,000 85 0.82 14,000 85 0.82 16,000 85 0.82 16,000 85 0.82 16,000 85 0.82 16.000 85 0.82 18.500

The technique described previously should result in an optimum design for any ESP application. As with other methods of equipment selection, however, motor starting must be examined. Eq. B-1 should be used to determine whether motor terminal voltage will be adequate at starting conditions. A value of Ivs exceeding 0.5 ensures dependable starting. 1

Practical Examples The techniques developed here have been used in seven practical examples. Design criteria for these examples have been chosen so that the results will illustrate various points made previously. A minimal power cost of $0.05/kW-hr has been assumed in all cases. Power costs exceeding twice this amount are common and would greatly magnify the results of these examples. The first three cases were the basis of the graphic illustrations presented in Figs. 2 through 7. The assumption that Pi and PI were equal or negligible was made for simplicity. Average conductor temperature of 140F [60C] was assumed in all examples except Case 7. Fluid specific gravities of 1.0 were assumed. except in Cases 5 through 7. Casing ID was not a constraint in Cases 1 through 4, which involved wells completed with 7-in. [17.8-cm] casing. Cases 5 through 7 used 5.5-in. [14.0-cm] casing. Data on the typical pumps and motors from which selections were made are illustrated in Tables 2 and 4, re-spectively. Presented in Table 5 are typical prices of tubing and power cable used in the examples. Total system costs presented in the various cases are for pump, motor, cable, and tubing only. Tubing and cable selection would have minimal effect on the cost of other components. These examples illustrate that the designs based on the technique presented here will generally differ from designs based on commonly used rules or the criteria of Ref. I. Table 6 compares the results using these three bases for all seven cases.

Case 1 (High RatelShallow Depth). The first three cases are based on identical net hydraulic loads. Case I presents a combination of a relatively large producing rate of 4,000 BID [636 m 3 /d] and a

TABLE 6-SUMMARV OF RESULTS OF PRACTICAL EXAMPLES

Economic Optimum Common Practice" Tubing Tubing Ref. 1

Case Size Cable Pr Size Cable Pr Payout t Cable Number ~ Size (kW) ~ Size (kW) (years) Size* ---

1 3.500 4 81.6222 3.500 6 82.7574 2.41 8 2 2.875 4 87.8751 2.375 6 95.9305 1.49 4 3 2.375 4 101.5222 2.375 6 106.9514 2.02 1 4 2.875 1 92.2510 2.375 2 100.4746 1.45 2/0 5 2.375 4 65.8538 2.375 6 69.7266 2.30 1/0 6 2.375 4 126.0527 2.375 6 130.6709 1.93 4 7 2.375 2"" 76.4487 2.375 2"" 76.4487 2/0

'Head loss less than 100 1t11.000 ft and voltage loss less than 30 VII ,000 ft. "Governed by motorstarting criteria.

t Economic optimum compared with common practice assuming a power cost of $0.05IkWhr. 'Ref. I limits voltage drop to 5% of motor nameplate and addresses tubing size only in regard to casing clearance.

222 SPE Production Engineering, May 1988

relatively shallow depth of 2,000 ft [610 m]. These are the con-ditions on which Figs. 2 and 5 are based. The first step in designing an ESP system is to select an appropriate pump type. For this ap-plication, a 7.0-4000 pump was selected. This pump, designed for installation inside 7-in. [17.8-cm] or larger casing, develops 36 ft [11.0 m] of head per stage at a producing rate of 4,000 B/D [636 m3/d] and requires 1.559 hp/stage [1.163 kW/stage] when pumping at these conditions, assuming -y= 1.0. The smallest-diameter tubing that would result in a head loss of less than 100 ft/I,OOO ft [10 m/100 m] was tentatively selected. This criterion dictated the use of 3.5-in. [8.9-cm] tubing, which is the largest size recommended 1 for installation inside 7-in. [17.8-cm] casing and which develops a head loss of 48 ft/I,OOO ft [4.8 m/IOO m]. For the first trial, a Size 6 cable was investigated. From Table I, values for rk and K vat 140F [60C] of 0.489 and 0.744, respectively, may be observed. The first iteration resulted in a system that cost $39,340 and incorporated a 58-stage, Type 7.0-4000 pump and a lOO-hp [74.6-kW]/1,700-V/36-A Type 7.0 motor. Voltage drop per 1,000 ft [305 m] is the product of running amperage and K v' which in this trial equals 26.8 V/I,OOO ft [26.8 V/305 m]. Consequently, Size 6 cable would be selected if the commonly used criterion of 30 V/I,OOO ft [30 V/305 m] were used. A value of PT=82.7574 kW can be computed with Eq. A-lO for this initial design. Size 4 cable was investigated next and resulted in an additional cost of $1,200 and a value of PTof 81.6222 kW, representing a 1.1352-kW decrease. Assuming a power cost of $0.05/kW-hr, the addi-tional cost of the Size 4 cable would be recouped in a period of 2.41 years. Thus, Size 4 is preferable to Size 6, which would have commonly been selected. Use of Size 2 cable was similarly inves-tigated, and the recoupment period was found to be 9.21 years. Therefore, 3.5-in. [8.9-cm] tubing and Size 4 cable is the optimum combination for Case I. Application of Eq. B-1 indicates that motor starting is not a problem. The criteria of Ref. 1 would have dic-tated the use of Size 8 cable, if available.

As stated previously, it is unnecessary to investigate smaller tubing sizes if the initial selection was the smallest size that develops a head loss less than 100 ftl1,OOO ft [10 ml100 m]. This statement was verified for Case 1. A system using 2.875-in. [7.3-cm] tubing would result in a head loss of 120 ft/I,OOO ft [12 m/100 m], an initial cost saving of $2,480, and a power consumption of 87.3752 kW, representing an increase of 5.7530 kW. Assuming a power cost of $0.05/kW-hr, the additional cost of the system that uses 3.5-in. [8.9-cm] tubing would be recouped in a 0.98-year period.

Case 2 (Medium Rate/Medium Depth). Case 2 illustrates an ESP producing 2,000 BID [318 m3/d] from a depth of 4,000 ft [1219 m]. This medium-rate/medium-depth case was the basis for Figs. 3 and 6. A type 7.0-2000 pump was selected that develops 40 ft [12.2 m] of head per stage when operated at a rate of 2,000 BID [318 m3/d] and absorbs 0.920 hp/stage [0.686 kW/stage]. The in-itial tubing selection for this example was 2.375 in. [6.03 cm], which would result in a head loss of 95 ft/1,OOO ft [9.5 m/100 m]. The most economical design using this tubing size required a IIO-stage pump and a lOO-hp [74.6-kW]/1,700-V/36-A Type 7.0 motor that was slightly overloaded, used Size 4 cable, consumed 93.2335 kW, and cost $47,400. The second tubing selection was 2.875 in. [7.3 cm], which developed a head loss of 35 ft/I,OOO ft [3.5 ml100 m]. The most economical design subsequently developed required a 104-stage pump, used Size 4 cable, consumed 87.8751 kW, and cost $50,240. A system using 3.5-in. [8.9-cm] tubing that incurred a head loss of 13 ft/1 ,000 ft [1.3 m/100 m] was similarly developed. This design required a WI-stage pump, used Size 4 cable, con-sumed 85.9177 kW, and cost $56,060. The system using 2.875-in. [7.3-cm] tubing and Size 4 cable was found to be the optimum. The incremental cost compared with the system using 2.375-in. [6.03-cm] tubing would be recouped in a 1.21-year period, assuming a power cost of $0.050/kW-hr. A power cost of $0.113/kW-hr would be required to justify the system using 3.5-in. [8.9-cm] tubing. Application of Eq. B-1 indicates that motor starting would not be a problem for the selected system. By comparison, common practice would have dictated using 2.375-in. [6.03-cm] tubing and Size 6 cable, which would have resulted in a voltage drop of 26.8 V/l,OOO ft [26.8 V/305 m]. The additional cost of the optimum

SPE Production Engineering, May 1988

system compared with that selected by common practice would have been recouped in a period of 1.49 years. Size 4 cable would have been selected if the criteria of Ref. 1 were used.

Case 3 (Low Rate/Great Depth). An ESP producing 1,000 BID [159 m3/d] from a depth of 8,000 ft [2438 m] is illustrated in Case 3. This low-rate, deep application was the basis for Figs. 4 and 7. A Type 5.5-1000 pump was selected that develops 20 ft [6.1 m] of head per stage when operated at a rate of 1,000 BID [159 m3 /d] and consumes 0.254 hp/stage [0.189 kW/stage]. The smallest tubing size commonly used in ESP applications is 2.375 in. [6.03 cm]. Head loss for this size is 26 ftl1,OOO ft [2.6 m/100 m] at the design rate. Consequently, it was chosen for the first trial design. The most economical system using 2.375-in. [6.03-cm] tubing required a 411-stage pump and a l00-hp [74.6-kW]/1 ,700-V/36-A Type 7.0 motor that was slightly overloaded, used Size 4 cable, consumed 101.5222 kW, and cost $78,752. The next trial used 2.875-in. [7.30-cm] tubing, which developed a head loss of 10 ft/1,OOO ft [I m/100 m]. The most economical design for this tubing size required a 404-stage pump and the same motor as the previous trial, used Size 4 cable, consumed 99.7312 kW, and cost $84,928. A period of 7.87 years would be required to recoup the additional cost of the larger-tubing system, assuming a power cost of $0.05/kW-hr. Consequently, a system using 2.375-in. [6.03-cm] tubing and Size 4 cable would be optimum. Dependable starting was verified through Eq. B-1. Common practice would have dic-tated using the same size tubing with Size 6 cable, which would have resulted in a voltage drop of26.8 V/I,OOO ft [26.8 V/305 m]. The additional cost of Size 4 cable over Size 6 would have been recouped in a period of 2.02 years. The criteria of Ref. I would dictate the use of Size 1 cable, which would not be an economi-cally viable design.

Case 4 (Effect of Motor Voltage on Cable Selection). The con-ditions of Case 4 are identical to those of Case 2 and include the use of 2.875-in. [7.30-cm] tubing, which was found to be the op-timum size. In Case 2, ai, 700-V motor was used, and it was deter-mined that Size 4 cable was the optimum size, assuming a power cost of $0.050/kW-hr. Power consumption of this system was 87.8751 kW. To provide a 3-year recoupment period for the in-cremental cost of Size 2 cable, the power cost would have to be $0.143/kW-hr. Case 4 assumes that an 850-V motor is used. In this circumstance, using Size 4 cable would result in a power con-sumption of99.68l6 kW, compared with 94.3444 kW for Size 2 and 92.2510 kW for Size 1. Size 1 was found to be the optimum in this instance, providing a 2.62-year recoupment period for the incremental cost compared to Size 2, thus illustrating the effect of motor voltage on the choice of power cable.

Case 5 (Casing ID Constraint). Installing the selected equipment in the wellbores of the previous examples should present no problems. Frequently, however, the well casing ID becomes a con-straint. Presented in Case 5 is an ESP installation that has inherited a tubing string from the previous sucker-rod pumping system. The goal is to produce 750 BID [119 m3 /d] from a depth of 6,500 ft [1981 m]. Specific gravity of the well fluid is 1.05. The well is equipped with 5.5-in., 17-lbm/ft [14.0-cm, 25.3-kg/m] casing and 2.875-in. [7.3-cm] external upset tubing. The casing ID is 4.892 in. [12.43 cm], and the tubing coupling OD is 3.688 in. [9.368 cm], leaving a clearance of 1.204 in. [3.058 cm] for a power cable. Using the specified casing and 2.875-in. [7.3-cm] external upset or nonupset tubing, the largest recommended round cable is Size 6. 1 A full-length flat cable of larger size could be run; however, this should be done only in rare circumstances as a last resort be-cause of an inherent voltage imbalance. An ESP system was de-signed with the existing tubing, which consisted of a 262-stage Type 5.5-0750 pump, a 70-hp [52.2-kW]/1,150-V/38-A Type 5.5 motor and Size 6 cable. Total system cost was $66,722, including the value of the tubing. Cable voltage drop was 28.3 V/1,OOO ft [28.3 V/305 m], and system power consumption was 68.9473 kW. Next, a system with 2.375-in. [6.03-cm] tubing was designed that consisted of a 264-stage pump, the same motor as before, and Size 4 cable, which was determined to be the most economical. This system cost

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$65,484 and resulted in a power consumption of 65.8538 kW. As-suming that the two tubing strings involved in this comparison were of new-equipment value, the system using 2.375-in. [6.03-cm] tubing would have a $1,238 lower initial cost and cost $1 ,355/yr less to operate than the alternative system. Thus, it has been dem-onstrated that salvaging the tubing of the previous sucker-rod pump system resulted in an installation of superfluous flow capacity and insufficient current-carrying capacity. Common practice would have dictated a system with 2.375-in. [6.03-cm] tubing and Size 6 cable. Compared with this system, the additional cost of the recommended optimum would be recouped in a period of2.30 years. The criteria of Ref. I would dictate the use of Size 110 cable, which is neither commonly available nor economically viable.

Case 6 (Tubing/Cable Compromise). In the preceding example, it was obvious which of the two alternative systems was most de-sirable. This is not always the case. Case 6 involves the same con-ditions presented in Case 5, except that the well has now responded to enhanced recovery and is capable of producing 1,500 B/D [238 m3 /d]. At this rate, the head losses of 2.375- and 2.875-in. [6.03-and 7.3-cm] tubing are 56 and 21 ftll,OOO ft [5.6 and 2.1 m/loo m], respectively. The most economical system employing 2.375-in. [6.03-cm] tubing consisted of a 36 I-stage Type 5.5-1500 pump, a 130-hp [96.9-kW]/2,2oo-V/31-A motor, and Size 4 cable. This system cost $84,574 and consumed 126.0527 kW. A system using 2.875-in. [7.3-cm] tubing was restricted to Size 6 cable, included a 349-stage pump and the same motor as the preceding design, cost $85,466, and consumed 125.9265 kW. The system using 2.375-in. [6.03-cm] tubing is the one of choice because the recoupment period for the additional cost of the alternative system would be 16.14 years. The point illustrated here is that the power-consumption advantage afforded by the larger cable size in Case 5 has been es-sentially balanced by an increase in energy consumed by tubing friction as the flow rate increased from 750 to 1 ,500 BID [119 to 238 m3 /d]. At a slightly greater rate, the two designs would have equivalent economic impact, and at rates above that point, the use of2.875-in. [7.3-cm] tubing would be the economical choice. This illustrates the compromise that can occur as a result of casing ID constraint.

Case 7 (Verification of Motor Starting). It has been stated that the selection of the most economical cable size does not necessarily ensure dependable motor starting. Factors contributing to this cir-cumstance include low power cost and deep pump-setting depth. This point is demonstrated in Case 7, which concerns a well equipped with 5.5-in. [14.0-cm] casing and producing 600 BID [95.4 m3/d] from 11,000 ft [3353 m]. The well fluid has a spe-cific gravity of 0.9 and the average conductor temperature is 176F [80C]. From Table 1, values for rk of 0.522,0.329, and 0.212 and values for Kv of 0.792, 0.512, and 0.340 can be calculated for Sizes 6, 4, and 2 cable, respectively, at this temperature. It quickly becomes apparent that 2.375-in. [6.03-cm] tubing should be used. Equipment selected for this application includes a 427-stage Type 5.5-0600 pump and an 80-hp [59.7-kW]/1,300-V/39-A Type 5.5 motor. Power consumption for this system using Sizes 6,4, and 2 cable is 87.5944, 80.8400, and 76.4487 kW, respec-tively. The incremental cost of Size 4 cable compared with Size 6 would be recouped in a period of 2.23 years. The recoupment period for the additional cost of Size 2 cable over Size 4 is 8.01 years. Size 4 is the economically optimum cable size; however, dependable motor starting must be verified. Using Eq. B-1 and as-suming Fls =4, it was determined thativs =0.49, which is slightly below the threshold value for dependable motor starting. This oc-curred regardless of the use of a high-voltage motor and selection of the optimum cable size. Use of Size 2 cable would result in ivs =0.66, thus ensuring dependable starting. Under the circum-stances presented in this example, the starting characteristics of the specific motor should be investigated before cable selection.

Evaluating Quotations After well productivity has been analyzed and a tubing size selected, it is common practice to solicit competitive bids for the balance of the equipment required for a new ESP installation. Assuming

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that all proposed pumps and motors have approximately the same efficiencies, Eq. A-4 can be used to compare quickly the operating costs of various quoted systems. This is true because values of PH would be approximately the same and the only other component of P r is P e' A small sample of recent quotations was analyzed and approximately 50% of these proposed the cable size that would have been selected with the technique presented here, while the other 50% proposed a cable one size smaller. All quoted systems should have functioned satisfactorily. The quotations incorporating smaller cable were less expensive than the competing bids, but they were not the economical choice. This demonstrates that it is the con-sumer's responsibility to determine the combination of cable and tubing sizes that will result in minimum-cost operation.

Conclusions I. Standard bases for tubing and power-cable selection do not

ensure economical systems at current electric power costs. 2. Optimum ESP design requires concurrent evaluation of tubing

and power-cable sizes and a knowledge of motor-voltage availa-bility because of the interrelated effects of tubing friction, power-cable resistance, and motor voltage on power consumption.

3. Motors having the highest available nameplate voltage are the most desirable, and this desirability is magnified at greater depths and when smaller cable is used.

4. Minimizing power consumption requires operating a pump and motor at conditions of high efficiency and power factor.

5. Changing motor voltage can alter the optimum power-cable size.

6. Selection of ESP systems based on the optimization technique or on commonly used design criteria does not necessarily guarantee dependable motor starting.

7. Using the tubing size required for a replaced sucker-rod pumping installation may result in an ESP system of superfluous flow capacity and insufficient current-carrying capacity when casing ID becomes a constraint.

8. Power cable specified in competitive bids is likely to have been selected only on the basis of functionality and initial price.

9. Economical design of ESP systems is the responsibility of the consumer.

Nomenclature Ac = conductor area, circular mils [cm2] d t = tubing ID, in. [cm]

Dk = pump setting depth, 1,000 ft [305 m] Em = motor efficiency, fraction Ep = pump efficiency, fraction ivs = fraction of nameplate voltage available for starting,

fraction Fls = starting-current factor, dimensionless F p = power factor, fractional HL = head loss, ftll,OOO ft [m/looO m]

I = steady-state running current, A Kf = coefficient for specific fluid properties and flow rate K v = voltage-drop coefficient for three-phase system for

specific conductor size, composition, and temperature and at specific power factor, V/A/I,OOO ft [V/A/m]

Pi = pump inlet pressure, psi [kPa] Pt = surface tubing pressure, psi [kPa] P e = power loss in cable, kW Pf = power consumed by tubing friction, kW Ph = power required for net hydraulic load, kW PH = power required for total hydraulic load, kW P L = combined power loss from tubing friction and cable

resistance, kW P n = normalized total power consumption, dimensionless Pr = total power consumption, kW

q = pumping rate, BID [m3/d] r = resistance, n

rk = conductor resistance, nll,OOO ft [nl305 m] SPE Production Engineering, May 1988

T = temperature, of [0C] V m = motor nameplate voltage, V X = inductive reactance, n

Xk = cable inductive reactance, nJ 1,000 ft [nJ305 m] Z = impedance, n () = phase angle between applied voltage and current, or

cos -I F p, degrees [rad] 'Y = fluid specific gravity, dimensionless

Acknowledgment I thank Conoco Inc. for permission to publish this paper.

References 1. API RP 11 U, API Recommended Practice for Sizing and Selection of

Electric Submersible Pumps, first edition, API (June 20, 1984). 2. IEEE Std. 1018-1985, IEEE Recommended Practice for Specifying

Electric Submersible Pump Cable/Ethylene Propylene Rubber Insulation, Inst. of Electrical and Electronics Engineers (Dec. \8, 1984).

3. IEEE Std. 1019-1985, IEEE Recommended Practice for Specifying Electric Submersible Pump Cable/Polypropylene Insulation, Inst. of Electrical and Electronics Engineers (Dec. 18, 1984).

4. Marks, L.S.: Mechanical Engineers Handbook, sixth edition, McGraw-Hill Book Co. Inc., New York City (1958) 15-6 and 15-7.

5. Vandevier, J.E.: "Procedure for Calculating Motor Starting Conditions for Electric Submersible Pump Installations," paper presented at the 1985 SPE Gulf Coast Section ESP Workshop, April 9-10.

6. Hyde, R.L. and Brinner, T.R.: "Starting Characteristics of Electric Submergible Oil Well Pumps," Trans., IEEE (Jan.-Feb. 1986) JA-22, No. I, \33-44.

Appendix A-Derivation of PowerConsumptlon Equation Power Required for Net Hydraulic Load. The rate of performing useful work (net hydraulic load) equals the product of producing rate, net lift, and fluid density. Electric power required for the net hydraulic load is this product divided by both pump and motor ef-ficiencies:

Power Consumed by Tubing Friction Loss. Tubing-friction-loss data are commonly presented in feet per 1,000 ft. The product of this value, pump setting depth expressed in thousands of feet, producing rate, and fluid density equals the frictional load. Electric power required is this product divided by both pump and motor efficiencies:

Total Hydraulic Load. The total hydraulic load is the sum of the net hydraulic and frictional loads. The resultant power requirement represents the motor input power and is expressed in Eq. A-3, which was obtained by adding Eqs. A-I and A-2:

.................................. (A-3)

Power-Cable Loss. Power-cable loss in a balanced three-phase system can be expressed as

Pe=3xlO-3Dkf2rk' ............................ (A-4) Motor input power (Eq. A-3) can be expressed as

p H =.J3 XIO- 3VmIFp . .......................... (A-5)

SPE Production Engineering, May 1988

Solving Eq. A-5 for I results in the following:

PHx 103 1= ................................... (A-6)

V3VmFp Substituting the preceding expression for I into Eq. A-4 yields

the following relationship between P e and PH'

Eq. A-8, a more detailed expression for Pe , was derived by sub-stituting the value of PH from Eq. A-3 into Eq. A-7:

................................. (A-8)

Combined Power Loss. The following expression for both tubing friction and cable-resistance power losses was developed by adding Eqs. A-2 and A-8:

1.268 x 1O-5q(0.433'YDkHL) PL =--------------------

EpEm

1.608 X 10-7 Dkrkq2[pt -Pi +0.433'YDk(1,OOO+Hd]2 +----------------------------------------

................................. (A-9)

Power-Consumption Equation. Total power consumption is the sum of Ph, Pi' and Pe; PH and Pe; or Ph and PL' Eq. A-1O was obtained by adding Eqs. A-3 and A-8:

1.268 x 1O-5q[Pt-pi+0.433'YDk(1 ,OOO+HL)] EpEm

................................ (A-IO)

Normalized Power. Normalized total power consumption is de-fined as Pr+Ph . Therefore, Eq. A-I I was developed by dividing Eq. A-1O by Eq. A-I:

................................. (A-II)

Appendix B-Derlvatlon of MotorStartlng Equation A minimum of 50% of nameplate voltage is required at the motor terminals to ensure dependable starting. 1 An inrush current equivalent to three to five times steady-state running current occurs the instant a submersible motor is energized, resulting in a cable voltage drop equal to F[sDkK vI. Because the no-load voltage would have been preadjusted to a level equal to Vm+DkKVI, Eq. B-1 describes the fraction of nameplate voltage available for starting,

225

ignoring transformer impedance losses and sag in the primary system:

D kK vl(F/s -l) fvs=l- .......................... (B-l) Vm

Substituting the value of I expressed in Eq. A-6 into Eg. B-1 yields

Eg. B-3 was obtained by solving Eg. B-2 for Kv:

Eq. B-4 was obtained by solving Eq. B-2 for Vm:

Appendix C-Sample Calculation of Serial Power Factor A l00-hp [74.6-kW]/1,150-V/56-A motor is to be set at 4,000 ft [1219 m] and operated fully loaded. Motor power factor at full load is 0.81. Size 4 copper cable is to be used. What is the system power factor?

Analysis of Motor Impedance to Neutral.

Z=Vm /l-13 =1,150/56-13 =11.8560.

cos 0=0.81; 0=35.904 [0.627 rad]; sin 0=0.5864.

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r= 11.856xO.81 =9.6040.

X= 11.856xO.5864=6.9520.

Calculation of Cable Resistance and Reactance.

r=4xrk=4xO.308= 1.2320.

X=4XXk =4xO.0399=0.1600.

Calculation of System Power Factor.

r=9.604+ 1.232= 10.8360.

X=6.952+0.160=7.1120.

0=tan- 1(7.1l2/1O.836)=33.278 [0.581 rad].

Fp=cos 0=0.836.

Thus, the cable impedance resulted in a system power factor that exceeded the motor power factor by 0.026, or 3.21 %.

51 Metric Conversion Factors bbl x 1.589 873 E-Ol m3

cycles/sec x 1.0* E+OO Hz ft x 3.048* E-Ol m

of (OF - 32)/1.8 C hp x 7.46043 E-Ol kW in. x 2.54* E+OO cm

lbm/ft x 1.488 164 E+OO kg/m mil x 2.54* E-05 m

Conversion factor is exact. SPEPE Original SPE manuscript received for review Oct. 5, 1986. Paper accepted for publication June 5, 1987. Revised manuscript received June 29, 1987. Paper (SPE 15423) first presented at the 1986 SPE Annual Technical Conference and Exhibition held in New Orleans, Oct. 5-8.

SPE Production Engineering, May 1988